A hydrostatic power transmission which uses hydraulic pump/motors and is employed as a continuously variable transmission has been known. This transmission has the advantage that speed can be continuously varied. However, it does not always have a high efficiency. Further, the range of speeds is not satisfactorily broad. Accordingly, a hydromechanical transmission (HMT) has been developed in which such a hydrostatic power transmission (HST) is used in conjunction with differential gearing. In such a transmission, the function of the transmission of power is divided between the HST and the differential gearing in order to achieve a high transmission efficiency of the gearing as well as the continuous variableness of the HST. See Chieo Ishihara: "Hydrodynamic Engineering," Asaka-shobo, Japan, and Sadao Ishihara: "Theory and Practice of Piston Pump Motor," Corona-sha, Japan. Also, the present inventor and others are developing a simple HMT as shown in FIG. 3. This HMT and the conventional HMT are so designed to change the displacements of a hydraulic pump/motor and to switch the transmission between low-speed and high-speed modes, for attaining high efficiency over broad ranges of speeds. However, these HMTs suffer from a deterioration in efficiency in the high-speed mode as described later.